President Donald Trump's promise to spend $1 trillion on infrastructure won applause Tuesday night in his first joint address to Congress, but has added to growing concerns on Capitol Hill about how he -- and lawmakers -- will pay for it.

The call to spend $1 trillion comes on top of announced plans to increase defense spending by $54 billion, plans to build a border wall that could cost upward of $20 billion and pay billions more in tax credits as part of a health care replacement plan.

"Budget-wise there's some real challenges there. I mean, he's talking about a huge infrastructure program, huge increases for defense, other huge expenditures, all while cutting taxes. All of which I like, but you've got to find a way to not blow the deficit to creation," said Rep. Hal Rogers, the former chairman of the House Appropriations Committee and a veteran spending hawk. "It's a big challenge."

The infrastructure plan carries an eye-popping price tag, but Republicans played down that cost Wednesday, saying that much of it would likely be covered by private investment and supported by measures like government-backed loans -- a favorite tool for energy programs and transportation projects.

The infrastructure details have not been hashed out yet in large part because congressional Republicans and the White House have been focused almost exclusively on the Obamacare replacement plan -- which is scheduled for a public crafting session in the House next week.

Members of the Republican Study Committee met privately Wednesday to hash out their stances on health care -- "drawing lines in the sand" on tax credits and spending, according to one attendee. Meanwhile, top Republicans trekked to the White House to discuss health care with Trump and Vice President Mike Pence.

Conservatives worried about increasing the nation's $20 trillion debt -- an issue Trump played up prominently during the campaign -- have been voicing their concerns around the Capitol.

Any program that increases budget deficits is "something a lot of us will resist," said Sen. Jeff Flake, an Arizona Republican.

A top House Republican aide downplayed concerns over spending for all of Trump's priorities, saying that any infrastructure plan would be "fiscally conservative" and noted that some of the conservatives now opposing health care tax credits signed onto 2015 legislation that included tax credits.

Until health care is dealt with, many Republicans say infrastructure will have to wait.

Democrats tried to force the issue last month with the introduction of legislation that called for $1 trillion in government spending for infrastructure -- but their measure has been on the back burner.

"I think at the end of the day offsetting increased spending is going to be a priority and we're not going to be able to cheat at all," Sen. Lindsey Graham, a South Carolina Republican, said Wednesday.

To get there, Trump's budget director, the newly-confirmed Mick Mulvaney, has proposed deep cuts to agencies including the Environmental Protection Agency and the State Department -- the cuts to the latter prompted Graham to declare Trump's budget "DOA" if he guts State's budget.

Asked Wednesday if Trump could find enough budget cuts throughout the government to cover the increased spending he wants, Graham simply said, "No."

Republican leaders said that they are hopeful that Trump's ascendancy will alleviate some of these concerns through a booming economy -- something they estimate could pull trillions of dollars into government coffers.

"Growth in the economy is ultimately the way a lot of this changes," said Sen. John Thune, the third-ranking Republican in the Senate. "If you take a 1% change in the GDP, that generates about a $300-billion-a-year difference in federal tax revenue, or $3 trillion over a decade. So I think that the president, his policies are going to lead to regrowth, and I hope if we can get these policies enacted, he'll be right about that."